Average Error: 17.2 → 0.0
Time: 2.4s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[y \cdot x + y \cdot \left(-z\right)\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
y \cdot x + y \cdot \left(-z\right)
double f(double x, double y, double z) {
        double r540065 = x;
        double r540066 = y;
        double r540067 = r540065 * r540066;
        double r540068 = r540066 * r540066;
        double r540069 = r540067 + r540068;
        double r540070 = z;
        double r540071 = r540066 * r540070;
        double r540072 = r540069 - r540071;
        double r540073 = r540072 - r540068;
        return r540073;
}
↓
double f(double x, double y, double z) {
        double r540074 = y;
        double r540075 = x;
        double r540076 = r540074 * r540075;
        double r540077 = z;
        double r540078 = -r540077;
        double r540079 = r540074 * r540078;
        double r540080 = r540076 + r540079;
        return r540080;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original17.2
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.2

    \[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]

  2. Simplified0.0

    \[\leadsto \color{blue}{y \cdot \left(x - z\right)}\]
  3. Using strategy rm

  4. Applied sub-neg0.0

    \[\leadsto y \cdot \color{blue}{\left(x + \left(-z\right)\right)}\]

  5. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{y \cdot x + y \cdot \left(-z\right)}\]

  6. Final simplification0.0

    \[\leadsto y \cdot x + y \cdot \left(-z\right)\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"
  :precision binary64

  :herbie-target
  (* (- x z) y)

  (- (- (+ (* x y) (* y y)) (* y z)) (* y y)))